1. ## Joint probability table

hi i have this question but am unsure about the table could some one please check if this correct thanks!!!!

Two players, A and B, play a rolling dice game. The player whose turn it is chooses wheather to roll one or two dice. if the total showing on the dice is even, the player who rolled them wins that amount of money from the other player, but if the toatal is odd he pays that amount to the other player.

i) Player A always rolls one die. Let Y denote the score on the die, X the net amound Player A wins, so that X=Y if is even, X=-Y if Y is odd.
a)Write down in tabular from the joint probabilty function of x and y.

Player B allways rolls 2 dice. Let the random variable U denote player Bs net gain when he rolls the dice
iia)Calculate the mean and variance of U
iib)In ten sucessive rolls of the dice by player B, What is the probability that the player gets at least seven even scores?

iii)The player rolls alternatly,each making 10 rolls.At the End of that time Player A calculates his net gain G=X(1)-U(1)+X(2)-U(2) +...+ X(10)-U(10). Write down the expectation and variance of G and hence calculate ({apporximatly)) the prob that player A loses money on the game.

Thanks really need help on this guys any thing will do!!!!!

2. Originally Posted by rishul
hi i have this question but am unsure about the table could some one please check if this correct thanks!!!!

Mr F says: There's nothing to check .....?? Only questions ..... Where exactly are you stuck?

Two players, A and B, play a rolling dice game. The player whose turn it is chooses wheather to roll one or two dice. if the total showing on the dice is even, the player who rolled them wins that amount of money from the other player, but if the toatal is odd he pays that amount to the other player.

i) Player A always rolls one die. Let Y denote the score on the die, X the net amound Player A wins, so that X=Y if is even, X=-Y if Y is odd.
a)Write down in tabular from the joint probabilty function of x and y.

Player B allways rolls 2 dice. Let the random variable U denote player Bs net gain when he rolls the dice
iia)Calculate the mean and variance of U
iib)In ten sucessive rolls of the dice by player B, What is the probability that the player gets at least seven even scores?

iii)The player rolls alternatly,each making 10 rolls.At the End of that time Player A calculates his net gain G=X(1)-U(1)+X(2)-U(2) +...+ X(10)-U(10). Write down the expectation and variance of G and hence calculate ({apporximatly)) the prob that player A loses money on the game.

Thanks really need help on this guys any thing will do!!!!!
..

7ia) E(x)=0.5 and Var(x)=14.9
7ic) E(xy)=3.5 hence Cov(xy)=0.265
7iia) E(u)=0 and E(u^2)= 54.83333... hence VAR(U)=54.833333
7iib) P(even) = 0.5 hence p(odd)=0.5
using binomial expansion from 10C7 to 10C8, adding all answers i obtained for the probabilty for at least seven even scores to be 0.17188

7iii) for this i was very stuck!!! using the rules for linear combinations of norm distributed variables i obtained for the
E(G)=10E(x)-10E(U)
E(G)=(10 x 0.5) -(10 x 0)
E(G)=5-0 hence E(G)=0

For the var(10(X1) - 10(u1))
=(10^2 x Var(x)) + (10^2 x var(u))
=(100 * 14.9) + (100 x 54.833)
=1490 + 5483.3333
=6973.3

but after this for the hence part i have no idea how no incoperate these values in to finding a probability. I think my values for e(g) are correct.

Thanks